You're going to need a table to sell the Lemonade on, Lemonade, a pitcher, plastic cups, a cash box and change. Make sure that someone is always watching your kids while they are selling the Lemonade. There are some shady people out there.
Lemonade stands do not require many supplies; you will need a large table and several chairs. You should purchase as much lemonade mix as you think you will need, along with sugar, water, ice cubes, cups, and straws, if you would like. To make signs, buy posterboard and poster paint. The last thing you need is a money box!
Whether using a table or a complete stand, try to provide the kids some shade with trees or a canopy. Make a nice sign with the price on it for the stand, and some small signs to put on the ends of your street. And you'll need dozens of lemons, a bag of sugar, a pitcher, wooden spoon, and cups.